Optimal streaks in a Falkner-Skan boundary layer

This paper deals with the optimal streaky perturbations (which maximize the perturbed energy growth) in a wedge flow boundary layer. These three dimensional perturbations are governed by a system of linearized boundary layer equations around the Falkner-Skan base flow. Based on an asymptotic analysis of this system near the free stream and the leading edge singularity, we show that for acute wedge semi-angle, all solutions converge after a streamwise transient to a single streamwise-growing solution of the linearized equations, whose initial condition near the leading edge is given by an eigenvalue problem first formulated in this context by Tumin (2001). Such a solution may be regarded as a streamwise evolving most unstable streaky mode, in analogy with the usual eigenmodes in strictly parallel flows, and shows an approximate self-similarity, which was partially known and is completed in this paper. An important consequence of this result is that the optimization procedure based on the adjoint equations heretofore used to define optimal streaks is not necessary. Instead, a simple low-dimensional optimization process is proposed and used to obtain optimal streaks. Comparison with previous results by Tumin and Ashpis (2003) shows an excellent agreement. The unstable streaky mode exhibits transient growth if the wedge semi-angle is smaller than a critical value that is slightly larger than $\pi/6$, and decays otherwise. Thus the cases of right and obtuse wedge semi-angles exhibit less practical interest, but they show a qualitatively different behavior, which is briefly described to complete the analysis

Comment on "Two Phase Transitions in the Fully frustrated XY Model"

The conclusions of a recent paper by Olsson (Phys. Rev. Lett. 75, 2758 (1995), cond-mat/9506082) about the fully frustrated XY model in two dimensions are questioned. In particular, the evidence presented for having two separate chiral and U(1) phase transitions are critically considered.Comment: One page one table, to Appear in Physical Review Letter

Charge-Vortex Duality in Double-Layered Josephson Junction Arrays

A system of two parallel Josephson junction arrays coupled by interlayer capacitances is considered in the situation where one layer is in the vortex-dominated and the other in the charge-dominated regime. This system shows a symmetry (duality) of the relevant degrees of freedom, i.e. the vortices in one layer and the charges in the other. In contrast to single-layer arrays both contribute to the kinetic energy. The charges feel the magnetic field created by vortices, and, vice versa, the vortices feel a gauge field created by charges. For long-range interaction of the charges the system exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and another one for charges. The interlayer capacitance suppresses both transition temperatures. The charge-unbinding transition is suppressed already for relatively weak coupling, while the vortex-unbinding transition is more robust. The shift of the transition temperature for vortices is calculated in the quasi-classical approximation for arbitrary relations between the capacitances (both weak and strong coupling).Comment: 12 pages, Revtex 3.

A short proof that the Coulomb-gauge potentials yield the retarded fields

A short demonstration that the potentials in the Coulomb gauge yield the retarded electric and magnetic fields is presented. This demonstration is relatively simple and can be presented in an advanced undergraduate curse of electromagnetic theory

Dissociation of vortex stacks into fractional-flux vortices

We discuss the zero field superconducting phase transition in a finite system of magnetically coupled superconducting layers. Transverse screening is modified by the presence of other layers resulting in topological excitations with fractional flux. Vortex stacks trapping a full flux and present at any finite temperature undergo an evaporation transition which corresponds to the depairing of fractional-flux vortices in individual layers. We propose an experiment with a bi-layer system allowing us to identify the dissociation of bound vortex molecules.Comment: 4 pages, 1 figure; revised version, to appear in Phys. Rev. Let

Electromagnetic effects of neutrinos in an electron gas

We study the electromagnetic properties of a system that consists of an electron background and a neutrino gas that may be moving or at rest, as a whole, relative to the background. The photon self-energy for this system is characterized by the usual transverse and longitudinal polarization functions, and two additional ones which are the focus of our calculations, that give rise to birefringence and anisotropic effects in the photon dispersion relations. Expressions for them are obtained, which depend on the neutrino number densities and involve momentum integrals over the electron distribution functions, and are valid for any value of the photon momentum and general conditions of the electron gas. Those expressions are evaluated explicitly for several special cases and approximations which are generally useful in astrophysical and cosmological settings. Besides studying the photon dispersion relations, we consider the macroscopic electrodynamic equations for this system, which involve the standard dielectric and permeability constants plus two additional ones related to the photon self-energy functions. As an illustration, the equations are used to discuss the evolution of a magnetic field perturbation in such a medium. This particular phenomena has also been considered in a recent work by Semikoz and Sokoloff as a mechanism for the generation of large-scale magnetic fields in the Early Universe as a consequence of the neutrino-plasma interactions, and allows us to establish contact with a specific application in a well defined context, with a broader scope and from a very different point of view.Comment: Revtex 20 page

Quantum-to-classical crossover for Andreev billiards in a magnetic field

We extend the existing quasiclassical theory for the superconducting proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry breaking magnetic field. Random-matrix theory (RMT) breaks down once the Ehrenfest time $\tau_E$ becomes longer than the mean time $\tau_D$ between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as $\tau_E/\tau_D$ is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model (the Andreev kicked rotator).Comment: 11 pages, 10 figure

Viscoelasticity and metastability limit in supercooled liquids

A supercooled liquid is said to have a kinetic spinodal if a temperature Tsp exists below which the liquid relaxation time exceeds the crystal nucleation time. We revisit classical nucleation theory taking into account the viscoelastic response of the liquid to the formation of crystal nuclei and find that the kinetic spinodal is strongly influenced by elastic effects. We introduce a dimensionless parameter \lambda, which is essentially the ratio between the infinite frequency shear modulus and the enthalpy of fusion of the crystal. In systems where \lambda is larger than a critical value \lambda_c the metastability limit is totally suppressed, independently of the surface tension. On the other hand, if \lambda < \lambda_c a kinetic spinodal is present and the time needed to experimentally observe it scales as exp[\omega/(\lambda_c-\lambda)^2], where \omega is roughly the ratio between surface tension and enthalpy of fusion

Suppression of Superconductivity in Mesoscopic Superconductors

We propose a new boundary-driven phase transition associated with vortex nucleation in mesoscopic superconductors (of size of the order of, or larger than, the penetration depth). We derive the rescaling equations and we show that boundary effects associated with vortex nucleation lowers the conventional transition temperature in mesoscopic superconductors by an amount which is a function of the size of the superconductor. This result explains recent experiments in small superconductors where it was found that the transition temperature depends on the size of the system and is lower than the critical Berezinsk\u{i}-Kosterlitz-Thouless temperature.Comment: To appear in Phys. Rev. Lett. Vol. 86 (15 Jan. 2001